Method of forming light modulating signal for displaying 3d image, and apparatus and method for displaying 3d image

ABSTRACT

A method of forming a light modulating signal for displaying a 3D includes preparing a plurality of data sets for 2D image data with different viewpoints; imposing a phase value the plurality of data sets, by which each of the 2D images is seen at a corresponding viewpoint; and superposing the 2D images.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority from Korean Patent Application No.10-2015-0027263, filed on Feb. 26, 2015, in the Korean IntellectualProperty Office, the disclosure of which is incorporated herein in itsentirety by reference.

BACKGROUND

1. Field

Apparatuses and methods consistent with exemplary embodiments relate todisplaying a three-dimensional (3D) image.

2. Description of the Related Art

A glasses system and a glassesless system have been widelycommercialized and used as methods of realizing a 3D image. The glassessystem includes a polarization glasses system and a shutter glassessystem, and the glassesless system includes a lenticular system and aparallax barrier system. Such systems use a binocular parallax betweenthe eyes, and, thus, there is a problem in that there is a limit in anumber of viewpoints, and further a viewer may feel fatigued due to amismatch between a depth appreciated in the brain and an eye focus.Thus, when a user focuses the eyes on a screen, the user can see thescreen with a good resolution and contrast but may feel fatigued due toa mismatch between a recognition position and the eye focus. Meanwhile,when the user focuses the eyes on a recognition position, the usercannot accurately see the screen due to a blurred screen.

Recently, research with respect to a multi-view type 3D display or aholographic 3D display has been performed to reduce the feeling of thefatigue.

The multi-view type 3D display provides 3D images with differentviewpoints to a plurality of visual fields, respectively. The number ofviewpoints may be increased to provide a natural motion parallax, and asa result, a resolution of unit viewpoint may be decreased.

The holographic 3D display provides a full parallax in which the depthappreciated in the brain and the eye focus are matched. The holographicdisplay system uses a principle of reproducing an original object imagewhen a hologram pattern is irradiated with the reference light anddiffracted in which an interference fringe obtained by interferingobject light reflected from an original object and a reference light isrecorded. The holographic display system which has been put to practicaluse would provide a computer generated hologram (CGH) toward a spacelight modulator as an electrical signal rather than obtain the hologrampattern by directly exposing the original object. The space lightmodulator forms the hologram pattern according to the input CGH signaland diffracts the reference light, to thereby generate a 3D image.However, a space light modulator with very high resolution and a greatamount of data processing are needed to realize a good holographicdisplay system.

SUMMARY

Exemplary embodiments address at least the above problems and/ordisadvantages and other disadvantages not described above. Also, theexemplary embodiments are not required to overcome the disadvantagesdescribed above, and may not overcome any of the problems describedabove.

One or more exemplary embodiments provide methods and apparatuses forforming a light modulating signal for displaying a 3D image, anddisplaying the 3D image.

According to an aspect of an exemplary embodiment, a method of forming alight modulating signal for displaying a 3D image includes preparing aplurality of data sets regarding two-dimensional (2D) image data withdifferent viewpoints; determining a phase value with respect to each ofthe 2D images, by which each of the 2D images is seen at a correspondingviewpoint; imposing a predetermined phase value to each of the pluralityof data sets regarding 2D images, and superposing the plurality of datasets regarding 2D images on which the phase value has been imposed; andconverting a complex function value obtained from the superposing intoan operating signal for a space light modulator.

The preparing the plurality of data sets regarding 2D images may includeconversion of format of 3D image data.

The preparing the plurality of data sets regarding 2D images may includecapturing the 2D images with different viewpoints by using cameras.

The preparing the plurality of data sets regarding 2D images may includeconverting light field data.

The preparing the plurality of data sets regarding 2D images and thedetermining the phase value may provide at least two 2D images withdifferent viewpoints to a pupil of a viewer.

The determining the phase value may use data calculated and stored inadvance with respect to various positions of a viewer's pupil.

According to an aspect of an exemplary embodiment, a method ofdisplaying a 3D image includes emitting a convergent coherent lighttoward a space light modulator; forming a light modulating signal fordisplaying the 3D image according to the above-described method; andmodulating light incident to the space light modulator according to thelight modulating signal.

The preparing the plurality of data sets regarding 2D images may includeconversion of format of 3D image data.

The preparing the plurality of data sets regarding 2D images may includecapturing the 2D images with different viewpoints by using cameras.

The preparing the plurality of data sets regarding 2D images may includeconverting light field data.

The preparing the plurality of data sets regarding 2D images and thedetermining the phase value may provide at least two 2D images withdifferent viewpoints to a pupil of a viewer.

The method of displaying the 3D image may further include eye trackingconfigured to sense a position of a viewer's pupil.

The determining the phase value may use data calculated and stored inadvance with respect to various positions of the viewer's pupil.

The emitting the convergent coherent light may adjust a direction alongwhich the light is emitted such that the light is converged toward thesensed position of the viewer's pupil.

The eye tracking may sense positions of left and right eyes of a viewer;and the emitting the convergent coherent light may adjust a directionalong which the light is emitted such that the light is converged towardthe left and right eyes of the viewer based on a time division method.

According to an aspect of another exemplary embodiment, a method offorming a light modulating signal for displaying a 3D image may includepreparing a plurality of data sets regarding 2D images with differentdepth cues; imposing a phase value to each of the plurality of data setsregarding 2D images, by which each of the 2D images is seen at aposition of a viewer's pupil; determining a conversion function by whichthe 2D image are provided at plurality of positions in the viewer'spupil, applying the conversion function to the plurality of data sets,and superposing the plurality of data sets to which the conversionfunction has been applied; and converting a complex function valueobtained from the superposing into an operating signal for a space lightmodulator.

According to an aspect of another exemplary embodiment, an apparatus fordisplaying a 3D image may include a backlight unit configured to emit aconvergent coherent light; a space light modulator configured tomodulate the light emitted from the backlight unit; a light modulatingsignal generator configured to generate a light modulating signal fordisplaying a 3D image according to the above-described method; and acontroller configured to control the space light modulator according tothe light modulating signal.

The apparatus for displaying a 3D image may further include an eyetracker configured to sense positions of left and right eyes of aviewer.

A converging direction of light emitted from the backlight unit may beadjusted according to the positions of the left and right eyes of theviewer.

The light modulating signal generator may generate a light modulatingsignal for odd-numbered frames and a light modulating signal foreven-numbered frames; and the controller may control the space lightmodulator to modulate light according to the light modulating signal forthe odd-numbered frames and the light modulating signal for theeven-numbered frames based on a time division method, and may controlthe backlight unit such that the light output from the backlight unit isconverged toward the left and right eyes of the viewer, insynchronization with the space light modulator.

The backlight unit may include first and second light sources configuredto output light in different directions and adjust output directions;and an optical lens configured to converge the light output from thefirst and second light sources.

The backlight unit may include a light source; a light guiding memberconfigured to include an incident surface on which light emitted fromthe light source is incident, a first surface from which the incidentlight is emitted, and a second surface facing the first surface; atleast one optical element configured to converge light; and a beamsteering element disposed between the light source and the incidentsurface of the light guiding member and adjust an angle at which thelight emitted from the light source is incident on the incident surface.

An output pattern emitting light from the light guiding member may beformed on the first surface or the second surface.

The at least one optical element may be a hologram optical elementdisposed on the first surface, the hologram optical element beingconfigured to emit light incident to the light guiding member in a formof convergent light.

The light guiding member is wedge shaped and a distance between thefirst and second surfaces is narrower farther from the light sourceunit, and may further include an inverted-prism sheet disposed on thefirst surface; a variable optical element disposed on the inverted-prismsheet; and an optical lens disposed on the variable optical element.

The space light modulator may be an amplitude modulation type spacelight modulator; and the controller may generate the light modulatingsignal by using a real part of a complex function value.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and/or other aspects will become more apparent by describingcertain exemplary embodiments with reference to the accompanyingdrawings, in which:

FIG. 1 is a sectional view of a schematic structure of a 3D imagedisplay apparatus according to an exemplary embodiment;

FIG. 2 is a flow chart schematically illustrating a process of forming alight modulating signal to be provided toward a space light modulator;

FIG. 3 is a schematic view of a method of obtaining prism phases to beprovided to each of a plurality of data sets regarding 2D image datawith different viewpoints;

FIG. 4 is a sectional view of a schematic structure of a 3D imagedisplay apparatus according to an exemplary embodiment;

FIG. 5 is a block diagram of a schematic structure of the 3D imagedisplay apparatus;

FIG. 6 is a flow chart schematically illustrating a process of forming alight modulating signal to be provided toward a space light modulator;

FIGS. 7A, 7B, and 7C are exemplary views of a light modulating signalforming process;

FIGS. 8A and 8B are exemplary views of synchronization of a direction oflight output from a backlight unit with a corresponding light modulatingsignal;

FIG. 9 is a sectional view of a schematic structure of a 3D imagedisplay apparatus according to an exemplary embodiment;

FIG. 10 is a sectional view of a schematic structure of a 3D imagedisplay apparatus according to an exemplary embodiment;

FIG. 11 is a sectional view of a schematic structure of a 3D imagedisplay apparatus according to an exemplary embodiment;

FIG. 12 is a flow chart schematically illustrating a process of forminga light modulating signal according to an exemplary embodiment; and

FIG. 13 is a block diagram of a schematic structure of the 3D imagedisplay apparatus according to an exemplary embodiment.

DETAILED DESCRIPTION

Certain exemplary embodiments are described in greater detail below withreference to the accompanying drawings.

In the following description, like drawing reference numerals are usedfor like elements, even in different drawings. The matters defined inthe description, such as detailed construction and elements, areprovided to assist in a comprehensive understanding of the exemplaryembodiments. However, it is apparent that the exemplary embodiments maybe practiced without those specifically defined matters. Also,well-known functions or constructions are not described in detail sincethey would obscure the description with unnecessary detail.

As used herein, the term “and/or” includes any and all combinations ofone or more of the associated listed items. Expressions such as “atleast one of,” when preceding a list of elements, modify the entire listof elements and do not modify the individual elements of the list.

FIG. 1 is a sectional view of a schematic structure of a 3D imagedisplay apparatus 1000 according to an exemplary embodiment. FIG. 2 is aflow chart schematically illustrating a process of forming a lightmodulating signal to be provided toward a space light modulator (SLM)130 in a light modulating signal generator 170 of the 3D image displayapparatus 1000 of FIG. 1. FIG. 3 is a schematic view of a method ofobtaining prism phases to be applied to each of a plurality set of dataregarding 2D image data with different viewpoints. The 3D image displayapparatus 1000 may include a backlight unit 100 and a space lightmodulator 130 modulating light from the backlight unit 100.

The 3D image display apparatus 1000 displays a plurality of images withdifferent viewpoints on a visual field of a viewer and provides astereoscopic effect. In forming the images with different viewpoints,the 3D image display apparatus 1000 according to an exemplary embodimentmay provide the space light modulator 130 with the light modulatingsignal by which at least two images are superposed and displayed on ascreen, thereby using the full resolution of the space light modulator130 and displaying a 3D image.

A controller 150 may control the space light modulator 130 according tothe light modulating signal formed in the light modulating signalgenerator 170. The light modulating signal transmitted from thecontroller 150 is a signal superposing and displaying at least twoimages with different viewpoints. When a coherent light is incident fromthe backlight unit 100 to the space light modulator 130, the superposedimages with different viewpoints are separated in the directions facingcorresponding viewpoints by diffraction. The images with differentviewpoints may be formed in a region that is smaller than the size ofthe pupil in a viewer's single eye, and thus the viewer may experiencethe stereoscopic effect only with the single eye. FIG. 1 illustratesthat the image is provided to three viewpoint positions. However, anexemplary embodiment is not limited thereto, and any number of viewpointpositions of two or greater may be used.

The backlight unit 100 may have various configurations capable ofemitting a convergent coherent light. For example, the backlight unit100 may include a light source and at least one convergent opticalelement. As the light incident from the backlight unit 100 to the spacelight modulator 130 is diffracted and modulated, and separates thesuperposed images into corresponding viewpoints, a laser light sourcehaving high coherence may be adapted in the backlight unit 100. A lightemitting diode (LED) may be adapted as a light source having spatialcoherence. In addition, a pin hole configuration or a lens may be usedto control the light of the light source so that a spatial coherence maybe improved. The pin hole configuration is known to those skilled in theart and, therefore, a detailed description is omitted. Furthermore,various light sources having good spatial coherence or optical devicescapable of improving spatial coherence of the light source may be usedby the configuration.

The space light modulator 130 may include at least one of a phasemodulator performing only phase modulation, an amplitude modulatorperforming only amplitude modulation, and a combined modulatorperforming both phase modulation and amplitude modulation. Furthermore,FIG. 1 illustrates the space light modulator 130 as a transmission typelight modulator but is not limited thereto, and a reflection type spacelight modulator may also be used. If the space light modulator 130 is atransmission type, a semiconductor modulator or a liquid crystal device(LCD) based on a compound semiconductor such as GaAs may be used. If thespace light modulator 130 is a reflection type, as for example, adigital micromirror device (DMD), a liquid crystal on silicon (LcoS) ora semiconductor modulator may be used.

The light modulating signal generator 170 may form a light modulatingsignal for displaying a 3D image.

By referring to FIG. 2, a light modulating signal forming method ofdisplaying a 3D image, which is performed in the light modulating signalgenerator 170, will be described.

First, a plurality of data sets regarding 2D image data with differentviewpoints is generated (operation 202). The plurality of data setsregarding 2D image data with different viewpoints may be obtained byvarious methods, as for example, by converting the format of a 3D imagedata. The 3D image data may be 3D model data, 3D computer graphic data,or color-depth data. The 3D image data may be data obtained by using a3D camera. A plurality of data sets regarding 2D image data withdifferent viewpoints may be obtained by converting light field dataobtained by using a light field camera.

Furthermore, the plurality set of data regarding 2D image data withdifferent viewpoints U₁ to U_(N) may be directly obtained by using aplurality of cameras (for example, N cameras).

For example, a plurality of data sets 204 regarding 2D images U₁ and U₂to U_(N) having a first viewpoint and second to an Nth viewpoint, e.g.,a first viewpoint and second to an Nth viewpoint 2D image data, may beprepared. The 2D images are to be provided to different viewpointpositions within a pupil and 3D images may be viewed when those imagesare combined.

Hereinafter, U_(j) represents ‘a data set regarding 2D image’ and may beabbreviated as ‘2D image data’. Furthermore, U_(j) may also represent animage displayed by 2D image data for convenience of explanation.

Next, respective directions in which each of the 2D images is to bedirected may be determined, for example, by calculating a prism phasefor each direction (operation 210). For example, a phase value by whicheach of the 2D images is seen at a corresponding viewpoint may bedetermined. The phase may be represented as a prism phase. By using aprinciple that the direction of light passing through a prism is changedaccording to an angle formed by a prism surface, a prism phasecorresponding to each of the first viewpoint to an Nth viewpoint 2Dimages U₁ to U_(N) may be imposed on corresponding 2D images so that theimages with different viewpoints may be focused on correspondingviewpoints. A prism phase φ_(j) corresponding to the 2D image data U_(j)may be represented as exp(iφ_(j)), which is a complex function. Aprocess for imposing the prism phase φ_(j) to the corresponding 2D imagedata U_(j) may be formed by operation such as U_(j)exp(iφ_(j)).

In operation 212, the 2D image data U_(j) on which the prism phase φ_(j)is imposed may be superposed or combined as follows:

$U = {\sum\limits_{j}{U_{j}{\exp \left( {\; \phi_{j}} \right)}}}$

Referring to FIG. 3, the prism phase φ_(j) corresponding to the 2D imagedata U_(j) may be determined as follows:

$\phi_{j} = {\frac{{2\pi}\;}{\lambda} \cdot \frac{\overset{\rightharpoonup}{R} \cdot \overset{\rightharpoonup}{K}}{F}}$

where F is a viewing distance, that is, a focal distance,

R is a vector toward each pixel from a center of a display panel,

K is a vector toward a viewing position from a focal position on a focalplane, and

λ is a wavelength of light transmitting corresponding pixel.

Superposed image data U may have a complex function value and convertedinto an operating signal, e.g., a light modulating signal, to be outputto the space light modulator 130, in operation 214. For example, thesuperposed image data U is digitized according to the number of pixelsof the space light modulator 130 and converted into a control signal tobe applied to each pixel. A processing method of the complex functionvalue may be changed according to the type of the space light modulator130. For example, when the space light modulator 130 is an amplitudemodulation type, a real part of the complex function may be used.

A signal generated from the light modulating signal generator 170 may beapplied to the space light modulator 130 through the controller 150.Light emitted from the backlight unit 100 may be diffracted andmodulated by passing through the space light modulator 130 in which thecontrol signal is applied, and may form images with different viewpointsin a viewer's visual field. Thus, a 3D image may be recognized by theviewer.

FIG. 4 is a sectional view of a schematic structure of a 3D imagedisplay apparatus 2000 according to an exemplary embodiment. FIG. 5 is ablock diagram of a schematic structure of the 3D image display apparatus2000 of FIG. 4. FIG. 6 is a flow chart schematically illustrating aprocess of forming a light modulating signal to be provided toward aspace light modulator 230 in a light modulating signal generator 270 ofthe three-dimensional image display apparatus 2000 of FIG. 4.

Referring to FIGS. 4 and 5, the 3D image display apparatus 2000 mayinclude a display panel 198, a backlight unit 200, the space lightmodulator 230, an eye tracker 290, the light modulating signal generator270, and a controller 250.

The backlight unit 200 may emit and provide a convergent coherent lightto the space light modulator 230, and may include a coherent lightsource, and at least one convergent optical element. The backlight unit200 may include a configuration such as a pin hole capable of improvingcoherence. The backlight unit 200 may have a configuration in which alight output direction is adjusted so that an output light may befocused on positions of left and right eyes of a viewer analyzed by theeye tracker 290. For example, a light output direction of the backlightunit 200 may be adjusted in a left-eye position and a right-eye positionby the controller 250.

The space light modulator 230 may use any one from among a phasemodulator performing only phase modulation, an amplitude modulatorperforming only amplitude modulation, and a combined modulatorperforming both phase modulation and amplitude modulation. Furthermore,FIG. 4 illustrates the space light modulator 230 as a transmission typelight modulator but is not limited thereto, a reflection type spacelight modulator is also available. If the space light modulator 230 is atransmission type, a semiconductor modulator based on a compoundsemiconductor such as GaAs or a LCD may be used. If the space lightmodulator 230 is a reflection type, for example, a DMD, a LcoS, or asemiconductor modulator may be used.

The eye tracker 290 senses a position of the viewer's pupil, and mayinclude an infrared camera, a visible ray camera, or other varioussensors. For example, the eye tracker 290 may obtain an image of theviewer by a camera and so on, and may detect a pupil of the viewer inthe image and analyze a position of the viewer's pupil. The position ofthe pupil may be predicted when the pupil of the viewer is not found dueto eye flickering or an obstacle, and a movement of the pupil positionmay be predicted according to a movement of the viewer. The eye tracker290 may track a position of the viewer's pupil change in real time andprovide the result to the controller 250. The controller 250 may providethe light modulating signal generator 270 with the pupil positiondetermined by the eye tracker 290, for a light modulating signalgeneration. The controller 250 may control the light output direction inthe backlight unit 200 to be focused on the pupil position determined bythe eye tracker 290.

The light modulating signal generator 270 may generate a lightmodulating signal for displaying the 3D image to operate the space lightmodulator 230 and transmit to the controller 250.

For example, the light modulating signal generator 270 may include a rawdata input unit 271, a viewpoints position determiner 273, a prism phasedeterminer 275, a data format converter 272, a prism phase encoder 276,and an SLM signal generator 277 for the SLM.

Raw data input to the raw data input unit 271 may include 3D image datahaving various formats. For example, 3D model data, 3D computer graphicdata, etc., may be input as the 3D image data. Various types of datacapable of displaying a 3D image such as a stereoscopic 3D image signal,or color-depth data obtained by using a 3D camera may be input.Furthermore, light field data obtained by using a light field camera maybe input. The raw input data may be input from a storage, memory, or aserver, or may be input as a live feed, e.g., from a camera.

A format of the input data may be converted by the data format converter272. For example, the input data may be converted into image data withdifferent viewpoints for a left eye and image data with differentviewpoints for a right eye as a plurality of data sets regarding 2Dimage data with different viewpoints.

In order to convert the data format, the viewpoints position determiner273 may determine viewpoint positions of images to be input to the pupilof the viewer based on the position of the pupil sensed by the eyetracker 290, and may transmit to the data format converter 272.

Considering the determined viewpoint positions, the data formatconverter 272 may convert the data format by using an operationprocessing method suitable for each type of the input image data. Forexample, the data may be converted into a plurality of data setsregarding directional images. The directional image signals may be aplurality of data sets regarding 2D image data with differentviewpoints, for example, image data with different viewpoints for a lefteye and image data with different viewpoints for a right eye. The imagedata with different viewpoints for the left eye may be first viewpoint2D image data U_(L1) for a left eye and second viewpoint 2D image dataU_(L2) for a left eye, to be provided to left and right sides of a pupilof the left eye, respectively. The image data with different viewpointsfor the right eye may be first viewpoint 2D image data U_(R1) for aright eye and second viewpoint 2D image data U_(R2) for a right eye, tobe provided to left and right sides of a pupil of the right eye,respectively.

FIG. 6 illustrates the data sets 602 converted by the data formatconverter 272 (operation 600). For example, the input data may beconverted into the first viewpoint 2D image data U_(L1) for the lefteye, the second viewpoint 2D image data U_(L2) for the left eye, thefirst viewpoint 2D image data U_(R1) for the right eye, and the secondviewpoint 2D image data U_(R2) for the right eye, but this is notlimited thereto, and the input data may be converted into otherappropriate image signals.

However, the raw data input unit 271 and the data format converter 272may be omitted in the light modulating signal generator 270. Forexample, four sets of data regarding images having different parallaxes,that is, the first viewpoint 2D image data U_(L1) for the left eye, thesecond viewpoint 2D image data U_(L2) for the left eye, the firstviewpoint 2D image data U_(R1) for the right eye, and the secondviewpoint 2D image data U_(R2) for the right eye may be obtained byusing two cameras for the left eye and two cameras for the right eye,respectively.

When the viewpoint positions are determined in the viewpoints positiondeterminer 273, a corresponding prism phase is determined by the prismphase determiner 275, in operation 604. For example, a prism phaseφ_(L1) corresponding to first viewpoint 2D image for a left eye, a prismphase φ_(L2) corresponding to a second viewpoint 2D image for a lefteye, a prism phase φ_(R1) corresponding to a first viewpoint 2D imagefor a right eye, and a prism phase φ_(R2) corresponding to a secondviewpoint 2D image for a right eye may be determined. The prism phasesmay be determined according to a position and a distance of a viewer'spupil. To reduce a calculation amount, all or a part of the prism phasesmay be stored in a lookup table and be used properly according to theposition of the viewer's pupil. Furthermore, an intermediate calculationvalue for a prism phase calculation may be stored in the lookup table.The prism phase determiner 275 may extract data from the stored lookuptable, e.g., from a memory 280, according to the position of theviewer's pupil. The extracted data may be converted into a prism phasemask to be multiplied to each component of the 2D image data by acomponent-wise method.

The prism phase encoder 276 may respectively impose the prism phasesφ_(L1), φ_(L2), φ_(R1), and φ_(R2) determined by the prism phasedeterminer 275 to the plurality of 2D image data sets U_(L1), U_(L2),U_(R1), and U_(R2) with different viewpoints that are output from thedata format converter 272 and superpose the 2D image data on which prismphases are respectively imposed, in operation 608.

The operation 608 may be performed to obtain a superposed image dataU_(L) for a left eye and a superposed image data U_(R) for a right eyeas follows:

$U_{L} = {\sum\limits_{j}{U_{Lj}{\exp \left( {\; \phi_{Lj}} \right)}}}$$U_{R} = {\sum\limits_{j}{U_{Rj}{\exp \left( {\; \phi_{Rj}} \right)}}}$

The superposed image data U_(L) for a left eye and the superposed imagedata U_(R) for a right eye may be quantized to a value corresponding tothe number of pixels of the space light modulator 230 and output to theSLM signal generator 277. That is, U_(L)+U_(R) matrix has complexnumbers which may be expressed as integers, for example, the valuesbetween 0 and 255 may be used.

The SLM signal generator 277 may convert the superposed image dataformed in the prism phase encoder 276 into signals for the space lightmodulator. For example, the SLM signal generator 277 may form controlsignals to be applied to each pixel so that the superposed images aredisplayed on the space light modulator 230. For example, the superposedimage data U_(L) for the left eye may be converted into a lightmodulating signal for an odd-numbered frame (operation 610), and thesuperposed image data U_(R) for the right eye may be converted into alight modulating signal for an even-numbered frame (operation 612).

The controller 250 may control the space light modulator 230 accordingto the control signal generated and transmitted from the SLM signalgenerator 277. The controller 250 may control the space light modulator230 to modulate light according to the light modulating signal for theodd-numbered frame and the light modulating signal for the even-numberedframe alternately based on a time division method which is known tothose skilled in the art. Moreover, the controller 250 may control thebacklight unit 200 so that a converging direction of light emitted fromthe backlight unit 200 may alternately be directed to various pupilpositions, that is, a right eye E_(R) position and a left eye E_(L)position, analyzed by the eye tracker 290. For example, the controller250 may control the space light modulator 230 and the backlight unit 200so that the light emitted from the backlight unit 200 may be incident tothe space light modulator 230 while being converged into the right-eyeposition when a control signal to display the superposed image for theright eye is applied to the space light modulator 230, and the lightemitted from the backlight unit 200 may be incident to the space lightmodulator 230 while being converged into the left-eye position when acontrol signal to display the superposed image for the left eye isapplied to the space light modulator 230.

FIGS. 7A to 7C are exemplary views of a light modulating signal formingprocess in which a plurality of data sets with different viewpoints arerespectively imposed with corresponding phase values of each of theviewpoints and the light modulating signal is formed by superposition ofthe 2D image data on which the phase values are respectively imposed.

FIG. 7A conceptually shows applying a prism phase φ_(R1) to a firstviewpoint image data U_(R1) for a right eye in the light modulatingsignal generator 270. The first viewpoint image data U_(R1) for theright eye is for an image to be provided to a left side of a pupil ofthe right eye, and the prism phase φ_(R1) is a phase value makes thefirst viewpoint image data U_(R1) for the right eye to be directed tothe left side of a pupil of the right eye. The prism phase φ_(R1) may beprepared in a shape of a prism phase mask. A square displayed on anupper portion of a left side of the prism phase mask is a partialenlarged view and exemplarily illustrates a shape of the prism phase.The prism phase may be added on corresponding position of the firstviewpoint image data U_(R1) for the right eye. For example, the firstviewpoint image data U_(R1) for the right eye and the prism phase maskmay be multiplied to each other, component-wise.

FIG. 7B is a schematic view of applying a prism phase φ_(R2) to a secondviewpoint image data U_(R2) for a right eye in the light modulatingsignal generator 270. The second viewpoint image data U_(R2) for theright eye is for an image to be provided to a right side of a pupil ofthe right eye, and have a predetermined parallax with the firstviewpoint image data U_(R1) for the right eye. The prism phase φ_(R2) isa phase value makes the second viewpoint image data U_(R2) for the righteye to be directed to the right side of a pupil of the right eye. Theprism phase φ_(R2) may be prepared in a shape of a prism phase mask. Asquare displayed on an upper portion of a left side of the prism phasemask is a partial enlarged view which exemplarily illustrates a shape ofthe prism phase. The prism phase φ_(R2) is different from the prismphase φ_(R1) corresponding to the first viewpoint image data U_(R1) forthe right eye of FIG. 7A. The prism phase may be added on correspondingposition of the second viewpoint image data U_(R2) for the right eye.For example, the second viewpoint image data U_(R2) for the right eyeand the prism phase mask may be multiplied to each other,component-wise.

FIG. 7C is an enlarged view of a triangle in a superposed image in whichthe first viewpoint image data U_(R1) for the right eye and the secondviewpoint image data U_(R2) for the right eye to which prism phasesφ_(R1) and φ_(R2) are respectively imposed, are superposed and a realpart is extracted. For example, FIG. 7C is an enlarged view of an imageaccording to Re(U_(R1)*exp(iφ_(R1))+U_(R2)*exp(iφ_(R2))). When a controlsignal is applied to display the superposed image on the space lightmodulator 230, light is diffracted and modulated from the backlight unit200, and the first viewpoint image data U_(R1) for the right eye and thesecond viewpoint image data U_(R2) for the right eye are provided to theleft and right sides of the pupil of the right eye, respectively. InFIG. 7C, the square is omitted for convenience.

The similar process may be performed with respect to images withdifferent viewpoints for a left eye.

FIGS. 8A and 8B are exemplary views of synchronization of a direction oflight output from a backlight unit 200 with a corresponding lightmodulating signal, and respective recognition of a 3D image in a lefteye and a right eye, in the 3D image display apparatus 2000 of FIG. 4.

In FIG. 8A, light in the backlight unit 200 is output and convergedtoward a viewer's right eye E_(R), and in accordance with the lightdescribed above, a light modulating signal displaying a superposed imagefor a right eye, that is,

$\sum\limits_{j}{U_{Rj}{\exp \left( {\; \phi_{Rj}} \right)}}$

may be input to the space light modulator 230. FIG. 8A exemplarilyillustrates that a control signal to the space light modulator 230 iscalculated by taking a real part of

$\sum\limits_{j}{U_{Rj}{\exp \left( {\; \phi_{Rj}} \right)}}$

on the assumption that the space light modulator 230 is an amplitudemodulation type, but an exemplary embodiment is not limited thereto. Thelight emitted from the backlight unit 200 in the converging directioninto the viewer's right eye E_(R) and entered the space light modulator230 may be diffracted and separated according to the control signalapplied to the space light modulator 230. Thus, a first viewpoint imagedata U_(R1) for a right eye and a second viewpoint image data U_(R2) fora right eye may be steered to left and right sides of a pupil of theright eye E_(R), respectively.

In FIG. 8B, light in the backlight unit 200 is output and convergedtoward a converging direction into a viewer's left eye E_(L), and alight modulating signal displaying a superposed image for a left eye,that is,

$\sum\limits_{j}{U_{Lj}{\exp \left( {\; \phi_{Lj}} \right)}}$

may be input to the space light modulator 230. FIG. 8B exemplarilyillustrates that a control signal to the space light modulator 230 iscalculated by taking a real part of

$\sum\limits_{j}{U_{Lj}{\exp \left( {\; \phi_{Lj}} \right)}}$

on the assumption that the space light modulator 230 is an amplitudemodulation type, but an exemplary embodiment is not limited thereto. Thelight emitted from the backlight unit 200 in the converging directioninto the viewer's left eye E_(L) and entered the space light modulator230 may be diffracted and separated according to the control signalapplied to the space light modulator 230. Thus, a first viewpoint imagedata U_(L1) for a left eye and a second viewpoint image data U_(L2) fora left eye may be steered to the left and right sides of a pupil of theleft eye E_(L), respectively.

As described above, images having different parallaxes may be providedby multiple wave-fronts to the viewer's eyes, and the images may berecognized by the viewer as a 3D image. The 3D image is not recognizedby a binocular parallax method, that is, a parallax between the left eyeand the right eye but recognized by parallaxes which are respectivelyprovided to the both eyes. Thus, there is no vergence-accommodationconflict which may occur when the 3D image is displayed by a binocularparallax method. Furthermore, as each of the wave-fronts is displayed onthe space light modulator 230 as a superposed image, the entireresolution of the space light modulator 230 may be used and theresolution is not reduced even if the number of viewpoints is increased.Furthermore, the amount of data processing may be decreased compared tothat of the holography method.

FIG. 9 is a sectional view of a schematic structure of a 3D imagedisplay apparatus 3000 according to an exemplary embodiment.

The 3D image display apparatus 3000 may include a backlight unit 300, aspace light modulator 230, an eye tracker 290, a light modulating signalgenerator 270, and a controller 250.

The backlight unit 300 may output light in different directions andinclude first and second light sources 310 and 320 configured to adjustan output direction, and an optical lens 350 converging the light outputfrom the first and second light sources 310 and 320.

The first and second light sources 310 and 320 may provide a coherentlight and include at least one of a laser light source and an LED as alight source having spatial coherence. In addition, a pin hole capableof improving spatial coherence may be used.

The optical lens 350 may be disposed between the first and second lightsources 310 and 320 and the space light modulator 230, and thus lightfrom the first light source 310 may incident on the space lightmodulator 230 in a converging direction into a left eye E_(L), and lightfrom the second light source 320 may incident on the space lightmodulator 230 in a converging direction into a right eye E_(R).

The optical lens 350 may have various forms capable of achieving theabove function. For example, the optical lens 350 is illustrated as asingle lens, but is not limited thereto, and may include a plurality oflenses. In FIG. 9, the optical lens 350 is disposed in a position inwhich a traveling path of light in the first light source 310 and atraveling path of light in the second light source 320 are overlapped,but is not limited thereto. The optical lens 350 may be respectivelydisposed on the traveling path of light in the first light source 310and the traveling path of light in the second light source 320.Furthermore, when lights from the first and second light sources 310 and320 are emitted as convergent light, the optical lens 350 may beomitted.

The controller 250 may adjust light emitting directions from the firstand second light sources 310 and 320 according to position informationabout the left eye E_(L) and the right eye E_(R) analyzed by the eyetracker 290. The controller 250 may synchronize superposed image signalsfor a left eye and for a right eye that are transmitted from the lightmodulating signal generator 270 with the turning on/off of the first andsecond light sources 310 and 320. For example, the controller 250 maycontrol the first and second light sources 310 and 320, so that lightmay be emitted from the first light source 310 and is not emitted fromthe second light source 320 when the superposed image signals for theleft eye are applied to the space light modulator 230, and light may beemitted from the second light source 320 and is not emitted from thefirst light source 310 when the superposed image signals for the righteye are applied to the space light modulator 230.

FIG. 10 is a sectional view of a schematic structure of a 3D imagedisplay apparatus according to an exemplary embodiment.

The 3D image display apparatus 4000 may include a backlight unit 400, aspace light modulator 230, an eye tracker 290, a light modulating signalgenerator 270, and a controller 250.

The backlight unit 400 may include a light source 410, a light guidingmember 430, and a beam steering element 420 adjusting an incident angleto the light guiding member 430 from the light source 410.

The light source 410 provides a coherent light and may include at leastone of a laser light source and an LED as a light source having spatialcoherence. Furthermore, a configuration such as a pin hole capable ofimproving spatial coherence may be used.

The light guiding member 430 may have a configuration in which lightincident the incident surface 450 travels in the light guiding member430 by total reflection and is emitted from an upper surface 452, i.e.,a first surface. A surface of the light guiding member 430 may have anelement by which total reflection condition is broken and the lighttraveling inside the light guiding member 430 can be emitted. Forexample, an output pattern emitting the incident light from the lightguiding member 430 may be formed on the upper surface or a lower surface454, i.e., a second surface, of the light guiding member 430.

The backlight unit 400 may further include at least one optical elementto converge light. In an exemplary embodiment, a hologram opticalelement 440 is disposed on the upper surface of the light guiding member430 so that light incident to the light guiding member 430 may beemitted from the light guiding member 430 as convergent light. Forexample, the hologram optical element 440 may have a hologram patternfor emitting and converging light.

Another hologram optical element (not shown) may further be formed inthe side of the light guiding member 430, that is, the incident surface450 on which light is incident from the light source 410. The hologramoptical element may have a hologram pattern, e.g., for a functioncapable of improving uniformity by changing a condition from an incidentlight to light capable of being coupled to the light guiding member 430and by uniformly extending the light.

The beam steering element 420 may adjust a light incident angle on theincident flight guiding member 430 so that light emitted from thebacklight unit 400 may be converged in the position of the right eyeE_(R) or the left eye E_(L).

The beam steering element 420 may have a reflecting surface which isrotationally driven, and may be, for example, a galvanometer mirror or apolygon mirror. As another example, the beam steering element 420 may bean electrowetting element or a grating element as a variable opticalelement in which a direction of the reflecting surface is electricallycontrolled.

The controller 250 may control an operation of the beam steering element420 so that a light emitting direction from the backlight unit 400 maybe adjusted according to position information about the left eye E_(L)and the right eye E_(R) analyzed by the eye tracker 290. The controller250 may synchronize superposed image signals for a left eye and for aright eye that are transmitted from the light modulating signalgenerator 270 with a direction of the beam steering element 420. Forexample, the controller 250 may control the beam steering element 420,so that the direction of the beam steering element 420 may be adjustedto converge the light emitted from the backlight unit 400 to the lefteye E_(L) position when the superposed image signals for the left eyeare applied to the space light modulator 230, and to converge the lightemitted from the backlight unit 400 to the right eye E_(R) position whenthe superposed image signals for the right eye are applied to the spacelight modulator 230.

FIG. 11 is a sectional view of a schematic structure of a 3D imagedisplay apparatus 5000 according to an exemplary embodiment.

The 3D image display apparatus 5000 may include a backlight unit 500, aspace light modulator 230, an eye tracker 290, a light modulating signalgenerator 270, and a controller 250.

The backlight unit 500 may include a light source 510, a light guidingmember 520, an inverted-prism sheet 530, a variable optical element 540,and an optical lens 550.

The light source 510 provides a coherent light and may include at leastone of a laser light source and an LED as a light source of spatialcoherence. In addition, a pin hole capable of improving spatialcoherence may be used.

The light guiding member 520 is wedge shaped and a distance betweenupper and lower surfaces of the light guiding member 520 is narrowerfarther away from the light source unit 510. For example, the lightguiding member 520 may be thinner farther away from the light sourceunit 510.

The inverted-prism sheet 530 may be formed to collimate light emittedfrom the light guiding member 520 to a parallel light.

The light guiding member 520 in a wedge type and the inverted-prismsheet 530 are an exemplary configuration in which light from the lightsource 510 is collimated and emitted, and may be changed to anothercomponent capable of providing the collimated light.

The variable optical element 540 is an optical element capable ofconverting and emitting an incident light direction, that is, an opticalelement capable of controlling a light refraction direction. Forexample, the variable optical element 540 may be an electrowettingelement electrically controlling a boundary surface of two media havingdifferent refractive index from each other and also electricallycontrolling the direction along which the incident light is refractedand emitted.

The optical lens 550 is for converging light and may include a pluralityof lenses even though one lens is illustrated as the optical lens 550 inFIG. 11. Furthermore, FIG. 11 illustrates a biconvex lens, but theoptical lens 550 is not limited thereto, and a Fresnel lens may also beused.

The direction of the incident light to the variable optical element 540may be adjusted according to an operation of the optical lens 550, andthe optical lens 550 may converge the light to a left eye E_(L) or aright eye E_(R).

The controller 250 may control the operation of the variable opticalelement 540 so that a light emitting direction from the backlight unit500 according to information about the left eye E_(L) position or theright eye E_(R) position determined by the eye tracker 290. Thecontroller 250 may synchronize superposed image signals for a left eyeand for a right eye that are generated and transmitted from the lightmodulating signal generator 270 with a refractive surface direction ofthe variable optical element 540. For example, the controller 250 maycontrol the variable optical element 540, so that the variable opticalelement 540 may be operated to converge the light emitted from thebacklight unit 500 to the left eye E_(L) position when the superposedimage signals for the left eye are applied to the space light modulator230, and to converge the light emitted from the backlight unit 500 tothe right eye E_(R) position when the superposed image signals for theright eye are applied to the space light modulator 230.

FIG. 12 is a flow chart schematically illustrating a process of forminga light modulating signal to be provided toward a space light modulatorin a light modulating signal generator 270 according to an exemplaryembodiment. FIG. 13 is a block diagram of a schematic structure of the3D image display apparatus 9000.

The 3D image display apparatus 9000 may include a display panel 198, abacklight unit 200, the space light modulator 230, an eye tracker 290,the light modulating signal generator 270, and a controller 250 whichare described in detail above with reference to FIGS. 5 and 6. The lightmodulating signal generator 270 includes a data input unit 616, aviewpoints position determiner 627, a prism phase determiner 625, a dataformat converter 620, a prism phase encoder 626, and an SLM signalgenerator 638 which have functions similar to those of the correspondingcomponents described above with reference to FIGS. 5 and 6 and, thus,repeated descriptions will be omitted.

As described above, according to exemplary embodiments, the lightmodulating signal generator 270 converts raw data of various formatsinto 2D images with different viewpoints, imposes a prism phase to the2D images, and forms superposed images by superposition of the 2D imageson which the prism phases are respectively imposed.

With reference to FIGS. 12 and 13, in the present exemplary embodiment,in operation 614, to form superposed image data, 3D image data having acolor-depth data format which is input into the data input unit 616, isconverted into a plurality of depth images, e.g., image data 618, withdifferent depth cues, by a depth data format converter 620.

The depth image data may be a first depth image data U_(LD1) for a lefteye and a second depth image data U_(LD2) for a left eye to an Nth depthimage data U_(LDN) for a left eye; and a first depth image data U_(RD1)for a right eye and a second depth image data U_(RD2) for a right eye toan Nth depth image data U_(RDN) for a right eye.

In operations 622 and 624, corresponding to each of the depth image datasets, the prism phase by which the 2D images are seen from a position ofa viewer's pupil may be determined, respectively, by a prism phasedeterminer 625. Further, prism phase φ_(L) may be applied to the depthimage data for a left eye, and prism phase φ_(R) may be applied to thedepth image data for a right eye, by a prism phase encoder 626.

Before superposing the depth images on which the prism phases areimposed, the depth images are converted to images with differentviewpoints, as determined by a viewpoints position determiner 627. Inoperation 628, a conversion function to be applied to each of the depthimage signals may be determined, by a conversion function determiner629.

For example, conversion functions T_(LD1) and T_(LD2) to T_(LDN) for theleft eye, and conversion functions T_(RD1) and T_(RD2) to T_(RDN) forthe right eye may be determined for the first depth image data U_(LD1)for the left eye to the Nth depth image data U_(LDN) for the left eye,respectively, and for the first depth image data U_(LD1) for the righteye to the Nth depth image data U_(LDN) for the right eye, respectively.

Next, to the depth image data U_(LDj) for a left eye on which prismphase φ_(L) is imposed, the conversion functions T_(LDj) arerespectively applied, and, to the depth image data U_(RDj) for a righteye on which prism phase φ_(R) is imposed, the conversion functionsT_(RDj) are respectively applied. For example, the conversion functionsmay be applied by the conversion function determiner 629.

In operation 630, superposition is performed to calculate superposedimage data U_(L) for left eye, by a superposed data generator 631, asfollows:

$U_{L} = {\sum\limits_{j}{T_{LDj}U_{LDj}{\exp \left( {\; \phi_{LDj}} \right)}}}$

Also, in operation 632, superposition is performed to calculatesuperposed image data U_(R) for left eye as follows:

$U_{R} = {\sum\limits_{j}{T_{RDj}U_{RDj}{\exp \left( {\; \phi_{RDj}} \right)}}}$

A superposed image data U_(L) for a left eye and a superposed image dataU_(R) for a right eye may be respectively converted into a lightmodulating signal for an odd-numbered frame (operation 634) and a lightmodulating signal for an even-numbered frame (operation 636), by an SLMsignal generator 638, and applied to the space light modulator.

In an exemplary embodiment, some of the components of the lightmodulating signal generator 270 may be omitted and the operationsdescribed above may be performed by a single component having one ormore processors. For example, operations 622, 624, 628, 630, and 632 maybe performed by the superposed data generator 631 having one or moreprocessors, but this is not limiting.

Such a method of a light modulating signal generation for displaying a3D image may be applied to the 3D image display apparatuses of exemplaryembodiments described above.

According to the method of the light modulating signal generation fordisplaying the 3D image, a light modulating signal for displaying a 3Dimage, which has a higher resolution compared to a super multi-viewdisplay and requires less processing compared to a holographic display,may be formed.

A 3D image display apparatus adapting the above method may be realizedby a simple configuration including a backlight unit and a space lightmodulator, and may provide a 3D image substantially reducing oreliminating fatigue of a viewer.

According to exemplary embodiments, the use of the parallax barrier anda lenticular lens may be avoided by using coherent light and prism phasewhich is imposed on directional image. Coherent light is interfered byprism phase, which is imposed on directional image, and, then, theinterfered light is directed to a corresponding viewpoint.

The 3D image display apparatus may be applied to a variety of electronicdevices, for example, a monitor, a TV, a mobile display apparatus, or amobile communication device.

Exemplary embodiments can be written as computer programs and can beimplemented in computers that execute the programs using acomputer-readable recording medium.

Examples of the computer-readable recording medium include magneticstorage media (e.g., ROM, floppy disks, hard disks, etc.), opticalrecording media (e.g., CD-ROMs, or DVDs), etc.

The foregoing exemplary embodiments and advantages are merely exemplaryand are not to be construed as limiting. The present teaching may bereadily applied to other types of apparatuses. Also, the description ofthe exemplary embodiments is intended to be illustrative, and not tolimit the scope of the claims, and many alternatives, modifications, andvariations will be apparent to those skilled in the art.

What is claimed is:
 1. A method of forming a light modulating signal fordisplaying a three-dimensional (3D) image, the method comprising:preparing a plurality of data sets corresponding to two-dimensional (2D)images with different viewpoints; determining a phase value with respectto each of the 2D images, by which each of the 2D images is seen at acorresponding viewpoint; imposing the determined phase value to theplurality of data sets, and superposing the plurality of data sets onwhich the phase value has been imposed; and converting a complexfunction value obtained from the superposing into an operating signalfor a space light modulator.
 2. The method of claim 1, wherein thepreparing the plurality of data sets comprises converting format ofinput 3D image data.
 3. The method of claim 1, wherein the preparing theplurality of data sets comprises capturing the 2D images with differentviewpoints by using cameras.
 4. The method of claim 2, wherein thepreparing the plurality of data sets comprises converting light fielddata.
 5. The method of claim 1, wherein the preparing the plurality ofdata sets and the determining the phase value provide at least two 2Dimages with different viewpoints to a pupil of a viewer.
 6. The methodof claim 1, wherein the determining the phase value comprisesdetermining the phase value based on data calculated and stored inadvance with respect to various positions of a viewer's pupil.
 7. Amethod of displaying a 3D image, the method comprising: emitting aconvergent coherent light toward a space light modulator; forming alight modulating signal for displaying the 3D image by using the methodof claim 1; and modulating light incident to the space light modulatoraccording to the light modulating signal.
 8. The method of claim 7,wherein the preparing the plurality of data sets comprises convertingformat of input 3D image data.
 9. The method of claim 7, wherein thepreparing the plurality of data sets comprises capturing the 2D imageswith different viewpoints by using cameras.
 10. The method of claim 7,wherein the preparing the plurality of data sets comprises convertinglight field data.
 11. The method of claim 7, wherein the preparing theplurality of data sets and the determining the phase value provide atleast two 2D images with different viewpoints to a pupil of a viewer.12. The method of claim 7, further comprising: performing an eyetracking configured to sense a position of a viewer's pupil.
 13. Themethod of claim 12, wherein the determining the phase value comprisesdetermining the phase value based on data calculated and stored inadvance with respect to various positions of the viewer's pupil.
 14. Themethod of claim 12, wherein the emitting the convergent coherent lightcomprises adjusting a direction along which the light is emitted suchthat the light is converged toward the sensed position of the viewer'spupil.
 15. The method of claim 12, wherein the performing the eyetracking comprises sensing positions of left and right eyes of a viewer,and the emitting the convergent coherent light comprises adjusting adirection along which the light is emitted such that the light isconverged toward the left and right eyes of the viewer based on a timedivision method.
 16. A method of forming a light modulating signal fordisplaying a three-dimensional (3D) image, the method comprising:preparing a plurality of data sets corresponding to two-dimensional (2D)images with different depth cues; imposing a phase value to each of theplurality of data sets, by which each of the 2D images is seen at acertain position in a viewer's pupil, of a plurality of positions;determining a conversion function by which the 2D images are provided atthe plurality of positions in the viewer's pupil; applying theconversion function to the plurality of data sets; superposing theplurality of data sets to which the conversion function has beenapplied; and converting a complex function value obtained from thesuperposing into an operating signal for a space light modulator.
 17. Anapparatus for displaying a 3D image, the apparatus comprising: abacklight unit configured to emit a convergent coherent light; a spacelight modulator configured to modulate the light emitted from thebacklight unit; a light modulating signal generator configured togenerate a light modulating signal for displaying a 3D image accordingto the method of claim 1; and a controller configured to control thespace light modulator according to the light modulating signal.
 18. Theapparatus of claim 17, further comprising: an eye tracker configured tosense positions of left and right eyes of a viewer.
 19. The apparatus ofclaim 18, wherein a converging direction of the light emitted from thebacklight unit is adjusted according to the positions of the left andright eyes of the viewer.
 20. The apparatus of claim 19, wherein thelight modulating signal generator is configured to generate the lightmodulating signal for odd-numbered frames and the light modulatingsignal for even-numbered frames, and the controller is configured tocontrol the space light modulator to modulate light according to thelight modulating signal for the odd-numbered frames and the lightmodulating signal for the even-numbered frames based on a time divisionmethod, and to control the backlight unit such that the light outputfrom the backlight unit is converged toward the left and right eyes ofthe viewer, in synchronization with the space light modulator.
 21. Theapparatus of claim 19, wherein the backlight unit comprises: first andsecond light sources configured to output light in different directionsand adjust output directions; and an optical lens configured to convergethe light output from the first and second light sources.
 22. Theapparatus of claim 19, wherein the backlight unit comprises: a lightsource; a light guiding member comprising an incident surface on whichthe light emitted from the light source is incident, a first surfacewhich is adjacent the incident surface and from which the incident lightis emitted, and a second surface opposing the first surface; at leastone optical element configured to converge light; and a beam steeringelement disposed between the light source and the incident surface ofthe light guiding member and configured to adjust an angle at which thelight emitted from the light source is incident on the incident surface.23. The apparatus of claim 22, wherein an output pattern configured toemit light from the light guiding member is formed on the first surfaceor the second surface.
 24. The apparatus of claim 22, wherein the atleast one optical element comprises a hologram optical element which isdisposed on the first surface, and is configured to emit light incidentto the light guiding member as a convergent light.
 25. The apparatus ofclaim 22, wherein the light guiding member is wedge shaped element inwhich a distance between the first and second surfaces becomes smalleras a distance from the light source unit becomes greater, and theapparatus further comprises: an inverted-prism sheet disposed on thefirst surface; a variable optical element disposed on the inverted-prismsheet; and an optical lens disposed on the variable optical element. 26.The apparatus of claim 17, wherein the space light modulator is anamplitude modulation space light modulator; and the controller isconfigured to generate the light modulating signal by using a real partof a complex function value.
 27. A non-transitory computer-readablestorage medium having recorded thereon software instructions which, whenexecuted by a computer system, cause the computer system to execute themethod of claim
 1. 28. A method comprising: obtaining data setscorresponding to two-dimensional (2D) images having different viewpointsin eyes of a viewer; determining phase values for the 2D images, bywhich each of the 2D images is seen at a corresponding viewpoint in theeyes of the viewer; applying the determined phase values to the datasets, respectively; calculating a complex function value by superposingthe data sets to which the phase values have been applied; convertingthe calculated complex function value into an operating signal for aspace light modulator; modulating light emitted from a backlight unitbased on the operating signal; and displaying the 2D images directed tothe different viewpoints in the eyes of the viewer by using themodulated light, thereby performing a display of a three-dimensionalimage as seen by the viewer.
 29. The method of claim 28, furthercomprising: sensing positions of pupils of the viewer; and determininglocations of the different viewpoints in the pupils of the viewer basedon the sensed positions of the pupils.
 30. The method of claim 29,wherein the phase values configured to adjust light directions in whichrespective 2D images are directed to be seen at corresponding viewpointsin the pupils of the viewer.